A270238 - OEIS

%I #37 Aug 15 2022 02:07:44

%S 1,4,7,23,41,79,89,97,127,167,191,223,239,241,257,281,439,577,593

%N Indices of Pell numbers of the form x^2 + xy + y^2.

%C Terms of this sequence are prime numbers most of the time.

%e 4 is a term because A000129(4) = 12 and 12 = 2^2 + 2*2 + 2^2.

%o (PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];

%o isA003136(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);

%o for(n=1, 1e3, if(isA003136(a000129(n)), print1(n, ", ")));

%Y Cf. A000129, A003136.

%K nonn,more

%O 1,2

%A _Altug Alkan_, Mar 18 2016

%E a(17)-a(19) from _Jinyuan Wang_, Aug 14 2022